Flexoelectrically Driven Electroclinic Effect in the Twist-Bend Nematic Phase of Achiral Molecules with Bent Shapes

We extend the twist-bend nematic ($N_{\mathrm{TB}}$) model to describe the electro-optics of this novel phase. We predict an electroclinic effect (ECE) subject to a dc electric field $\mathbf{E}$ applied perpendicular to the helix axis or wave vector $\mathbf{q}$, with rotation of the $N_{\mathrm{TB}}$ optic axis around $\mathbf{E}$. This linear effect, with its flexoelectric origin, is a close analog to the electro-optic effects observed for chiral liquid crystals. However, in nematics composed of achiral molecules having a bent shape, it is the electro-optic signature of the $N_{\mathrm{TB}}$ phase. We test our model experimentally in the low-temperature nematic phase of the odd liquid crystal dimer, CB7CB, with its molecules having, on average, a bent shape. The ECE measurements confirm the previously proposed twist-bend nematic structure of this phase, with its broken chiral symmetry, extremely short ($<10\mathrm{nm}$) doubly degenerate pitch and ultrafast, submicrosecond response times.

Figure 1

Spontaneous distortion of the $N_{\mathrm{TB}}$ phase: (a) Spatial arrangement of the bent molecules which are locally intercalated. (b) Director $\mathbf{n}$ (blue) and spontaneous bend $\mathbf{b}$ (red) in the conical twist-bend helix. (c) Trajectories of the $\mathbf{n}$ and $\mathbf{b}$ projections on the $\mathbf{x}\mathbf{y}$ plane. The arrows show the rotation direction for right-(R) and left-(L) handed helices. The sign of $\mathbf{b}$ is reversed with the handedness.

Figure 2

$N_{\mathrm{TB}}$ phase subject to an electric field $\mathbf{E}$ at a fixed wave vector $\mathbf{q}$: (a) Dielectric distortion of the $\mathbf{n}$ trajectory ($\Delta \epsilon >0$ is assumed). (b) Electroclinic effect due to the flexoelectric coupling. The director $\mathbf{n}(z)$ and the optic axis $\mathbf{N}$ (in green) are uniformly rotated around $\mathbf{E}$ with respect to the $E=0$ case (dashed line). (c) 3D geometry of the flexoelectric tilt of the twist-bend cone and the optic axis.

Figure 3

Electroclinic effect in the low-temperature nematic phase of CB7CB: (a),(b) Single domains observed with slightly uncrossed polarizers (white arrows); (c) Tilt angle $\alpha (t)$ determined with short square pulses ($\tau =10\mu \mathrm{s}$, $U=40\mathrm{V}$), shown at the start and end of the pulse with dashed lines. The relaxation times were obtained from an exponential fit (red and blue lines) of the data. (d) Tilt angles $\alpha (t)$ measured in two single domains with opposite handedness (black and blue data points) with triangular voltage pulses (red line), and (e) temperature dependence of the ECE tilt angle ($U=40\mathrm{V}$ square pulses, $d=1.6\mu \mathrm{m}$).